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Astronomy chapter 4

Chapter 4

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Astronomy chapter 4

  1. 1. Figure 3.14 Mathematicians Who Discovered a Planet. (a) John Couch Adams (1819–1892) and (b) Urbain J. J. Le Verrier (1811–1877) share the credit for discovering the planet Neptune. We should note that the discovery of Neptune was not a complete surprise to astronomers, who had long suspected the existence of the planet based on the “disobedient” motion of Uranus. On September 10, 1846, two weeks before Neptune was actually found, John Herschel, son of the discoverer of Uranus, remarked in a speech before the British Association, “We see [the new planet] as Columbus saw America from the shores of Spain. Its movements have been felt trembling along the far-reaching line of our analysis with a certainty hardly inferior to ocular demonstration.” This discovery was a major step forward in combining Newtonian theory with painstaking observations. Such work continues in our own times with the discovery of planets around other stars. L I N K T O L E A R N I N G For the fuller story of how Neptune was predicted and found (and the effect of the discovery on the search for Pluto), you can read this page (https://openstaxcollege.org/l/30nepplumatdis) on the mathematical discovery of planets. M A K I N G C O N N E C T I O N S Astronomy and the Poets When Copernicus, Kepler, Galileo, and Newton formulated the fundamental rules that underlie everything in the physical world, they changed much more than the face of science. For some, they gave humanity the courage to let go of old superstitions and see the world as rational and manageable; for Chapter 3 Orbits and Gravity 93
  2. 2. others, they upset comforting, ordered ways that had served humanity for centuries, leaving only a dry, “mechanical clockwork” universe in their wake. Poets of the time reacted to such changes in their work and debated whether the new world picture was an appealing or frightening one. John Donne (1573–1631), in a poem called “Anatomy of the World,” laments the passing of the old certainties: The new Philosophy [science] calls all in doubt, The element of fire is quite put out; The Sun is lost, and th’ earth, and no man’s wit Can well direct him where to look for it. (Here the “element of fire” refers also to the sphere of fire, which medieval thought placed between Earth and the Moon.) By the next century, however, poets like Alexander Pope were celebrating Newton and the Newtonian world view. Pope’s famous couplet, written upon Newton’s death, goes Nature, and nature’s laws lay hid in night. God said, Let Newton be! And all was light. In his 1733 poem, An Essay on Man, Pope delights in the complexity of the new views of the world, incomplete though they are: Of man, what see we, but his station here, From which to reason, to which refer? . . . He, who thro’ vast immensity can pierce, See worlds on worlds compose one universe, Observe how system into system runs, What other planets circle other suns, What vary’d being peoples every star, May tell why Heav’n has made us as we are . . . All nature is but art, unknown to thee; All chance, direction, which thou canst not see; All discord, harmony not understood; All partial evil, universal good: And, in spite of pride, in erring reason’s spite, One truth is clear, whatever is, is right. Poets and philosophers continued to debate whether humanity was exalted or debased by the new views of science. The nineteenth-century poet Arthur Hugh Clough (1819–1861) cries out in his poem “The New Sinai”: And as old from Sinai’s top God said that God is one, By science strict so speaks He now to tell us, there is None! Earth goes by chemic forces; Heaven’s a Mécanique Celeste! And heart and mind of humankind a watchwork as the rest! 94 Chapter 3 Orbits and Gravity This OpenStax book is available for free at http://cnx.org/content/col11992/1.13
  3. 3. (A “mécanique celeste” is a clockwork model to demonstrate celestial motions.) The twentieth-century poet Robinson Jeffers (whose brother was an astronomer) saw it differently in a poem called “Star Swirls”: There is nothing like astronomy to pull the stuff out of man. His stupid dreams and red-rooster importance: Let him count the star-swirls. Chapter 3 Orbits and Gravity 95
  4. 4. angular momentum aphelion apogee asteroid belt astronomical unit (AU) density eccentricity ellipse escape speed focus gravity Kepler’s first law Kepler’s second law Kepler’s third law major axis momentum Newton’s first law Newton’s second law Newton’s third law CHAPTER 3 REVIEW KEY TERMS the measure of the motion of a rotating object in terms of its speed and how widely the object’s mass is distributed around its axis the point in its orbit where a planet (or other orbiting object) is farthest from the Sun the point in its orbit where an Earth satellite is farthest from Earth the region of the solar system between the orbits of Mars and Jupiter in which most asteroids are located; the main belt, where the orbits are generally the most stable, extends from 2.2 to 3.3 AU from the Sun the unit of length defined as the average distance between Earth and the Sun; this distance is about 1.5 × 108 kilometers the ratio of the mass of an object to its volume in an ellipse, the ratio of the distance between the foci to the major axis a closed curve for which the sum of the distances from any point on the ellipse to two points inside (called the foci) is always the same the speed a body must achieve to break away from the gravity of another body (plural: foci) one of two fixed points inside an ellipse from which the sum of the distances to any point on the ellipse is constant the mutual attraction of material bodies or particles each planet moves around the Sun in an orbit that is an ellipse, with the Sun at one focus of the ellipse the straight line joining a planet and the Sun sweeps out equal areas in space in equal intervals of time the square of a planet’s orbital period is directly proportional to the cube of the semimajor axis of its orbit the maximum diameter of an ellipse the measure of the amount of motion of a body; the momentum of a body is the product of its mass and velocity; in the absence of an unbalanced force, momentum is conserved every object will continue to be in a state of rest or move at a constant speed in a straight line unless it is compelled to change by an outside force the change of motion of a body is proportional to and in the direction of the force acting on it for every action there is an equal and opposite reaction (or: the mutual actions of two bodies upon each other are always equal and act in opposite directions) 96 Chapter 3 Orbits and Gravity This OpenStax book is available for free at http://cnx.org/content/col11992/1.13
  5. 5. orbit orbital period (P) orbital speed perigee perihelion perturbation satellite semimajor axis velocity the path of an object that is in revolution about another object or point the time it takes an object to travel once around the Sun the speed at which an object (usually a planet) orbits around the mass of another object; in the case of a planet, the speed at which each planet moves along its ellipse the point in its orbit where an Earth satellite is closest to Earth the point in its orbit where a planet (or other orbiting object) is nearest to the Sun a small disturbing effect on the motion or orbit of a body produced by a third body an object that revolves around a planet half of the major axis of a conic section, such as an ellipse the speed and direction a body is moving—for example, 44 kilometers per second toward the north galactic pole SUMMARY 3.1 The Laws of Planetary Motion Tycho Brahe’s accurate observations of planetary positions provided the data used by Johannes Kepler to derive his three fundamental laws of planetary motion. Kepler’s laws describe the behavior of planets in their orbits as follows: (1) planetary orbits are ellipses with the Sun at one focus; (2) in equal intervals, a planet’s orbit sweeps out equal areas; and (3) the relationship between the orbital period (P) and the semimajor axis (a) of an orbit is given by P2 = a3 (when a is in units of AU and P is in units of Earth years). 3.2 Newton’s Great Synthesis In his Principia, Isaac Newton established the three laws that govern the motion of objects: (1) objects continue to be at rest or move with a constant velocity unless acted upon by an outside force; (2) an outside force causes an acceleration (and changes the momentum) for an object; and (3) for every action there is an equal and opposite reaction. Momentum is a measure of the motion of an object and depends on both its mass and its velocity. Angular momentum is a measure of the motion of a spinning or revolving object and depends on its mass, velocity, and distance from the point around which it revolves. The density of an object is its mass divided by its volume. 3.3 Newton’s Universal Law of Gravitation Gravity, the attractive force between all masses, is what keeps the planets in orbit. Newton’s universal law of gravitation relates the gravitational force to mass and distance: Fgravity = G M1 M2 R2 The force of gravity is what gives us our sense of weight. Unlike mass, which is constant, weight can vary depending on the force of gravity (or acceleration) you feel. When Kepler’s laws are reexamined in the light of Newton’s gravitational law, it becomes clear that the masses of both objects are important for the third law, which becomes a3 = (M1 + M2) × P2 . Mutual gravitational effects permit us to calculate the masses of astronomical objects, from comets to galaxies. Chapter 3 Orbits and Gravity 97
  6. 6. 3.4 Orbits in the Solar System The closest point in a satellite orbit around Earth is its perigee, and the farthest point is its apogee (corresponding to perihelion and aphelion for an orbit around the Sun). The planets follow orbits around the Sun that are nearly circular and in the same plane. Most asteroids are found between Mars and Jupiter in the asteroid belt, whereas comets generally follow orbits of high eccentricity. 3.5 Motions of Satellites and Spacecraft The orbit of an artificial satellite depends on the circumstances of its launch. The circular satellite velocity needed to orbit Earth’s surface is 8 kilometers per second, and the escape speed from our planet is 11 kilometers per second. There are many possible interplanetary trajectories, including those that use gravity- assisted flybys of one object to redirect the spacecraft toward its next target. 3.6 Gravity with More Than Two Bodies Calculating the gravitational interaction of more than two objects is complicated and requires large computers. If one object (like the Sun in our solar system) dominates gravitationally, it is possible to calculate the effects of a second object in terms of small perturbations. This approach was used by John Couch Adams and Urbain Le Verrier to predict the position of Neptune from its perturbations of the orbit of Uranus and thus discover a new planet mathematically. FOR FURTHER EXPLORATION Articles Brahe and Kepler Christianson, G. “The Celestial Palace of Tycho Brahe.” Scientific American (February 1961): 118. Gingerich, O. “Johannes Kepler and the Rudolphine Tables.” Sky & Telescope (December 1971): 328. Brief article on Kepler’s work. Wilson, C. “How Did Kepler Discover His First Two Laws?” Scientific American (March 1972): 92. Newton Christianson, G. “Newton’s Principia: A Retrospective.” Sky & Telescope (July 1987): 18. Cohen, I. “Newton’s Discovery of Gravity.” Scientific American (March 1981): 166. Gingerich, O. “Newton, Halley, and the Comet.” Sky & Telescope (March 1986): 230. Sullivant, R. “When the Apple Falls.” Astronomy (April 1998): 55. Brief overview. The Discovery of Neptune Sheehan, W., et al. “The Case of the Pilfered Planet: Did the British Steal Neptune?” Scientific American (December 2004): 92. Websites Brahe and Kepler Johannes Kepler: His Life, His Laws, and Time: http://kepler.nasa.gov/Mission/JohannesKepler/ (http://kepler.nasa.gov/Mission/JohannesKepler/) . From NASA’s Kepler mission. Johannes Kepler: http://www.britannica.com/biography/Johannes-Kepler (http://www.britannica.com/ 98 Chapter 3 Orbits and Gravity This OpenStax book is available for free at http://cnx.org/content/col11992/1.13
  7. 7. biography/Johannes-Kepler) . Encyclopedia Britannica article. Johannes Kepler: http://www-history.mcs.st-andrews.ac.uk/Biographies/Kepler.html (http://www- history.mcs.st-andrews.ac.uk/Biographies/Kepler.html) . MacTutor article with additional links. Noble Dane: Images of Tycho Brahe: http://www.mhs.ox.ac.uk/tycho/index.htm (http://www.mhs.ox.ac.uk/tycho/index.htm) . A virtual museum exhibit from Oxford. Newton Sir Isaac Newton: http://www-groups.dcs.st-and.ac.uk/~history//Biographies/Newton.html (http://www-groups.dcs.st-and.ac.uk/~history//Biographies/Newton.html) . MacTutor article with additional links. Sir Isaac Newton: http://www.luminarium.org/sevenlit/newton/newtonbio.htm (http://www.luminarium.org/sevenlit/newton/newtonbio.htm) . Newton Biography at the Luminarium. The Discovery of Neptune Adams, Airy, and the Discovery of Neptune: http://www.mikeoates.org/lassell/adams-airy.htm (http://www.mikeoates.org/lassell/adams-airy.htm) . A defense of Airy’s role by historian Alan Chapman. Mathematical Discovery of Planets: http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/ Neptune_and_Pluto.html (http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/ Neptune_and_Pluto.html) . MacTutor article. Videos Brahe and Kepler “Harmony of the Worlds.” This third episode of Carl Sagan’s TV series Cosmos focuses on Kepler and his life and work. Tycho Brahe, Johannes Kepler, and Planetary Motion: https://www.youtube.com/watch?v=x3ALuycrCwI (https://www.youtube.com/watch?v=x3ALuycrCwI) . German-produced video, in English (14:27). Newton Beyond the Big Bang: Sir Isaac Newton’s Law of Gravity: http://www.history.com/topics/enlightenment/ videos/beyond-the-big-bang-sir-isaac-newtons-law-of-gravity (http://www.history.com/topics/ enlightenment/videos/beyond-the-big-bang-sir-isaac-newtons-law-of-gravity) . From the History Channel (4:35). Sir Isaac Newton versus Bill Nye: Epic Rap Battles of History: https://www.youtube.com/ watch?v=8yis7GzlXNM (https://www.youtube.com/watch?v=8yis7GzlXNM) . (2:47). The Discovery of Neptune Richard Feynman: On the Discovery of Neptune: https://www.youtube.com/watch?v=FgXQffVgZRs (https://www.youtube.com/watch?v=FgXQffVgZRs) . A brief black-and-white Caltech lecture (4:33). COLLABORATIVE GROUP ACTIVITIES A. An eccentric, but very rich, alumnus of your college makes a bet with the dean that if you drop a baseball and a bowling ball from the tallest building on campus, the bowling ball would hit the ground first. Have your group discuss whether you would make a side bet that the alumnus is right. How would you decide Chapter 3 Orbits and Gravity 99
  8. 8. who is right? B. Suppose someone in your astronomy class was unhappy about his or her weight. Where could a person go to weigh one-fourth as much as he or she does now? Would changing the unhappy person’s weight have any effect on his or her mass? C. When the Apollo astronauts landed on the Moon, some commentators commented that it ruined the mystery and “poetry” of the Moon forever (and that lovers could never gaze at the full moon in the same way again). Others felt that knowing more about the Moon could only enhance its interest to us as we see it from Earth. How do the various members of your group feel? Why? D. Figure 3.12 shows a swarm of satellites in orbit around Earth. What do you think all these satellites do? How many categories of functions for Earth satellites can your group come up with? E. The Making Connections feature box Astronomy and the Poets discusses how poets included the most recent astronomical knowledge in their poetry. Is this still happening today? Can your group members come up with any poems or songs that you know that deal with astronomy or outer space? If not, perhaps you could find some online, or by asking friends or roommates who are into poetry or music. EXERCISES Review Questions 1. State Kepler’s three laws in your own words. 2. Why did Kepler need Tycho Brahe’s data to formulate his laws? 3. Which has more mass: an armful of feathers or an armful of lead? Which has more volume: a kilogram of feathers or a kilogram of lead? Which has higher density: a kilogram of feathers or a kilogram of lead? 4. Explain how Kepler was able to find a relationship (his third law) between the orbital periods and distances of the planets that did not depend on the masses of the planets or the Sun. 5. Write out Newton’s three laws of motion in terms of what happens with the momentum of objects. 6. Which major planet has the largest . . . A. semimajor axis? B. average orbital speed around the Sun? C. orbital period around the Sun? D. eccentricity? 7. Why do we say that Neptune was the first planet to be discovered through the use of mathematics? 8. Why was Brahe reluctant to provide Kepler with all his data at one time? 9. According to Kepler’s second law, where in a planet’s orbit would it be moving fastest? Where would it be moving slowest? 10. The gas pedal, the brakes, and the steering wheel all have the ability to accelerate a car—how? 11. Explain how a rocket can propel itself using Newton’s third law. 100 Chapter 3 Orbits and Gravity This OpenStax book is available for free at http://cnx.org/content/col11992/1.13
  9. 9. 12. A certain material has a mass of 565 g while occupying 50 cm3 of space. What is this material? (Hint: Use Table 3.1.) 13. To calculate the momentum of an object, which properties of an object do you need to know? 14. To calculate the angular momentum of an object, which properties of an object do you need to know? 15. What was the great insight Newton had regarding Earth’s gravity that allowed him to develop the universal law of gravitation? 16. Which of these properties of an object best quantifies its inertia: velocity, acceleration, volume, mass, or temperature? 17. Pluto’s orbit is more eccentric than any of the major planets. What does that mean? 18. Why is Tycho Brahe often called “the greatest naked-eye astronomer” of all time? Thought Questions 19. Is it possible to escape the force of gravity by going into orbit around Earth? How does the force of gravity in the International Space Station (orbiting an average of 400 km above Earth’s surface) compare with that on the ground? 20. What is the momentum of an object whose velocity is zero? How does Newton’s first law of motion include the case of an object at rest? 21. Evil space aliens drop you and your fellow astronomy student 1 km apart out in space, very far from any star or planet. Discuss the effects of gravity on each of you. 22. A body moves in a perfectly circular path at constant speed. Are there forces acting in such a system? How do you know? 23. As friction with our atmosphere causes a satellite to spiral inward, closer to Earth, its orbital speed increases. Why? 24. Use a history book, an encyclopedia, or the internet to find out what else was happening in England during Newton’s lifetime and discuss what trends of the time might have contributed to his accomplishments and the rapid acceptance of his work. 25. Two asteroids begin to gravitationally attract one another. If one asteroid has twice the mass of the other, which one experiences the greater force? Which one experiences the greater acceleration? 26. How does the mass of an astronaut change when she travels from Earth to the Moon? How does her weight change? 27. If there is gravity where the International Space Station (ISS) is located above Earth, why doesn’t the space station get pulled back down to Earth? 28. Compare the density, weight, mass, and volume of a pound of gold to a pound of iron on the surface of Earth. 29. If identical spacecraft were orbiting Mars and Earth at identical radii (distances), which spacecraft would be moving faster? Why? Figuring For Yourself 30. By what factor would a person’s weight be increased if Earth had 10 times its present mass, but the same volume? Chapter 3 Orbits and Gravity 101
  10. 10. 31. Suppose astronomers find an earthlike planet that is twice the size of Earth (that is, its radius is twice that of Earth’s). What must be the mass of this planet such that the gravitational force (Fgravity) at the surface would be identical to Earth’s? 32. What is the semimajor axis of a circle of diameter 24 cm? What is its eccentricity? 33. If 24 g of material fills a cube 2 cm on a side, what is the density of the material? 34. If 128 g of material is in the shape of a brick 2 cm wide, 4 cm high, and 8 cm long, what is the density of the material? 35. If the major axis of an ellipse is 16 cm, what is the semimajor axis? If the eccentricity is 0.8, would this ellipse be best described as mostly circular or very elongated? 36. What is the average distance from the Sun (in astronomical units) of an asteroid with an orbital period of 8 years? 37. What is the average distance from the Sun (in astronomical units) of a planet with an orbital period of 45.66 years? 38. In 1996, astronomers discovered an icy object beyond Pluto that was given the designation 1996 TL 66. It has a semimajor axis of 84 AU. What is its orbital period according to Kepler’s third law? 102 Chapter 3 Orbits and Gravity This OpenStax book is available for free at http://cnx.org/content/col11992/1.13
  11. 11. Chapter Outline 4.1 Earth and Sky 4.2 The Seasons 4.3 Keeping Time 4.4 The Calendar 4.5 Phases and Motions of the Moon 4.6 Ocean Tides and the Moon 4.7 Eclipses of the Sun and Moon Thinking Ahead If Earth’s orbit is nearly a perfect circle (as we saw in earlier chapters), why is it hotter in summer and colder in winter in many places around the globe? And why are the seasons in Australia or Peru the opposite of those in the United States or Europe? The story is told that Galileo, as he left the Hall of the Inquisition following his retraction of the doctrine that Earth rotates and revolves about the Sun, said under his breath, “But nevertheless it moves.” Historians are not sure whether the story is true, but certainly Galileo knew that Earth was in motion, whatever church authorities said. It is the motions of Earth that produce the seasons and give us our measures of time and date. The Moon’s motions around us provide the concept of the month and the cycle of lunar phases. In this chapter we examine some of the basic phenomena of our everyday world in their astronomical context. Figure 4.1 Southern Summer. As captured with a fish-eye lens aboard the Atlantis Space Shuttle on December 9, 1993, Earth hangs above the Hubble Space Telescope as it is repaired. The reddish continent is Australia, its size and shape distorted by the special lens. Because the seasons in the Southern Hemisphere are opposite those in the Northern Hemisphere, it is summer in Australia on this December day. (credit: modification of work by NASA) 4 EARTH, MOON, AND SKY Chapter 4 Earth, Moon, and Sky 103
  12. 12. 4.1 EARTH AND SKY Learning Objectives By the end of this section, you will be able to: Describe how latitude and longitude are used to map Earth Explain how right ascension and declination are used to map the sky In order to create an accurate map, a mapmaker needs a way to uniquely and simply identify the location of all the major features on the map, such as cities or natural landmarks. Similarly, astronomical mapmakers need a way to uniquely and simply identify the location of stars, galaxies, and other celestial objects. On Earth maps, we divide the surface of Earth into a grid, and each location on that grid can easily be found using its latitude and longitude coordinate. Astronomers have a similar system for objects on the sky. Learning about these can help us understand the apparent motion of objects in the sky from various places on Earth. Locating Places on Earth Let’s begin by fixing our position on the surface of planet Earth. As we discussed in Observing the Sky: The Birth of Astronomy, Earth’s axis of rotation defines the locations of its North and South Poles and of its equator, halfway between. Two other directions are also defined by Earth’s motions: east is the direction toward which Earth rotates, and west is its opposite. At almost any point on Earth, the four directions—north, south, east, and west—are well defined, despite the fact that our planet is round rather that flat. The only exceptions are exactly at the North and South Poles, where the directions east and west are ambiguous (because points exactly at the poles do not turn). We can use these ideas to define a system of coordinates attached to our planet. Such a system, like the layout of streets and avenues in Manhattan or Salt Lake City, helps us find where we are or want to go. Coordinates on a sphere, however, are a little more complicated than those on a flat surface. We must define circles on the sphere that play the same role as the rectangular grid that you see on city maps. A great circle is any circle on the surface of a sphere whose center is at the center of the sphere. For example, Earth’s equator is a great circle on Earth’s surface, halfway between the North and South Poles. We can also imagine a series of great circles that pass through both the North and South Poles. Each of this circles is called a meridian; they are each perpendicular to the equator, crossing it at right angles. Any point on the surface of Earth will have a meridian passing through it (Figure 4.2). The meridian specifies the east-west location, or longitude, of the place. By international agreement (and it took many meetings for the world’s countries to agree), longitude is defined as the number of degrees of arc along the equator between your meridian and the one passing through Greenwich, England, which has been designated as the Prime Meridian. The longitude of the Prime Meridian is defined as 0°. 104 Chapter 4 Earth, Moon, and Sky This OpenStax book is available for free at http://cnx.org/content/col11992/1.13
  13. 13. Figure 4.2 Latitude and Longitude of Washington, DC. We use latitude and longitude to find cities like Washington, DC, on a globe. Latitude is the number of degrees north or south of the equator, and longitude is the number of degrees east or west of the Prime Meridian. Washington, DC’s coordinates are 38° N and 77° W. Why Greenwich, you might ask? Every country wanted 0° longitude to pass through its own capital. Greenwich, the site of the old Royal Observatory (Figure 4.3), was selected because it was between continental Europe and the United States, and because it was the site for much of the development of the method to measure longitude at sea. Longitudes are measured either to the east or to the west of the Greenwich meridian from 0° to 180°. As an example, the longitude of the clock-house benchmark of the U.S. Naval Observatory in Washington, DC, is 77.066° W. Figure 4.3 Royal Observatory in Greenwich, England. At the internationally agreed-upon zero point of longitude at the Royal Observatory Greenwich, tourists can stand and straddle the exact line where longitude “begins.”(credit left: modification of work by “pdbreen”/Flickr; credit right: modification of work by Ben Sutherland) Your latitude (or north-south location) is the number of degrees of arc you are away from the equator along your meridian. Latitudes are measured either north or south of the equator from 0° to 90°. (The latitude of the equator is 0°.) As an example, the latitude of the previously mentioned Naval Observatory benchmark is 38.921° N. The latitude of the South Pole is 90° S, and the latitude of the North Pole is 90° N. Chapter 4 Earth, Moon, and Sky 105
  14. 14. Locating Places in the Sky Positions in the sky are measured in a way that is very similar to the way we measure positions on the surface of Earth. Instead of latitude and longitude, however, astronomers use coordinates called declination and right ascension. To denote positions of objects in the sky, it is often convenient to make use of the fictitious celestial sphere. We saw in Observing the Sky: The Birth of Astronomy that the sky appears to rotate about points above the North and South Poles of Earth—points in the sky called the north celestial pole and the south celestial pole. Halfway between the celestial poles, and thus 90° from each pole, is the celestial equator, a great circle on the celestial sphere that is in the same plane as Earth’s equator. We can use these markers in the sky to set up a system of celestial coordinates. Declination on the celestial sphere is measured the same way that latitude is measured on the sphere of Earth: from the celestial equator toward the north (positive) or south (negative). So Polaris, the star near the north celestial pole, has a declination of almost +90°. Right ascension (RA) is like longitude, except that instead of Greenwich, the arbitrarily chosen point where we start counting is the vernal equinox, a point in the sky where the ecliptic (the Sun’s path) crosses the celestial equator. RA can be expressed either in units of angle (degrees) or in units of time. This is because the celestial sphere appears to turn around Earth once a day as our planet turns on its axis. Thus the 360° of RA that it takes to go once around the celestial sphere can just as well be set equal to 24 hours. Then each 15° of arc is equal to 1 hour of time. For example, the approximate celestial coordinates of the bright star Capella are RA 5h = 75° and declination +50°. One way to visualize these circles in the sky is to imagine Earth as a transparent sphere with the terrestrial coordinates (latitude and longitude) painted on it with dark paint. Imagine the celestial sphere around us as a giant ball, painted white on the inside. Then imagine yourself at the center of Earth, with a bright light bulb in the middle, looking out through its transparent surface to the sky. The terrestrial poles, equator, and meridians will be projected as dark shadows on the celestial sphere, giving us the system of coordinates in the sky. The Turning Earth Why do many stars rise and set each night? Why, in other words, does the night sky seem to turn? We have seen that the apparent rotation of the celestial sphere could be accounted for either by a daily rotation of the sky around a stationary Earth or by the rotation of Earth itself. Since the seventeenth century, it has been generally accepted that it is Earth that turns, but not until the nineteenth century did the French physicist Jean Foucault provide an unambiguous demonstration of this rotation. In 1851, he suspended a 60-meter pendulum weighing about 25 kilograms from the dome of the Pantheon in Paris and started the pendulum swinging evenly. If Earth had not been turning, there would have been no alteration of the pendulum’s plane of oscillation, and so it would have continued tracing the same path. Yet after a few minutes Foucault could see that the pendulum’s plane of motion was turning. Foucault explained that it was not the pendulum that was shifting, but rather Earth that was turning beneath it (Figure 4.4). You can now find such pendulums in many science centers and L I N K T O L E A R N I N G You can explore a variety of basic animations about coordinates and motions in the sky at this interactive site (https://openstaxcollege.org/l/30anicoormot) from ClassAction. Click on the “Animations” tab for a list of options. If you choose the second option in the menu, you can play with the celestial sphere and see RA and declination defined visually. 106 Chapter 4 Earth, Moon, and Sky This OpenStax book is available for free at http://cnx.org/content/col11992/1.13
  15. 15. planetariums around the world. Figure 4.4 Foucault’s Pendulum. As Earth turns, the plane of oscillation of the Foucault pendulum shifts gradually so that over the course of 12 hours, all the targets in the circle at the edge of the wooden platform are knocked over in sequence. (credit: Manuel M. Vicente) Can you think of other pieces of evidence that indicate that it is Earth and not the sky that is turning? (See Collaborative Group Activity A at the end of this chapter.) 4.2 THE SEASONS Learning Objectives By the end of this section, you will be able to: Describe how the tilt of Earth’s axis causes the seasons Explain how seasonal differences on Earth vary with latitude One of the fundamental facts of life at Earth’s midlatitudes, where most of this book’s readers live, is that there are significant variations in the heat we receive from the Sun during the course of the year. We thus divide the year into seasons, each with its different amount of sunlight. The difference between seasons gets more pronounced the farther north or south from the equator we travel, and the seasons in the Southern Hemisphere are the opposite of what we find on the northern half of Earth. With these observed facts in mind, let us ask what causes the seasons. Many people have believed that the seasons were the result of the changing distance between Earth and the Sun. This sounds reasonable at first: it should be colder when Earth is farther from the Sun. But the facts don’t bear out this hypothesis. Although Earth’s orbit around the Sun is an ellipse, its distance from the Sun varies by only about 3%. That’s not enough to cause significant variations in the Sun’s heating. To make matters worse for people in North America who hold this hypothesis, Earth is actually closest to the Sun in January, when the Northern Hemisphere is in the middle of winter. And if distance were the governing factor, why would the two hemispheres have opposite seasons? As we shall show, the seasons are actually caused by the 23.5° tilt of Earth’s axis. Chapter 4 Earth, Moon, and Sky 107
  16. 16. The Seasons and Sunshine Figure 4.5 shows Earth’s annual path around the Sun, with Earth’s axis tilted by 23.5°. Note that our axis continues to point the same direction in the sky throughout the year. As Earth travels around the Sun, in June the Northern Hemisphere “leans into” the Sun and is more directly illuminated. In December, the situation is reversed: the Southern Hemisphere leans into the Sun, and the Northern Hemisphere leans away. In September and March, Earth leans “sideways”—neither into the Sun nor away from it—so the two hemispheres are equally favored with sunshine. Figure 4.5 Seasons. We see Earth at different seasons as it circles the Sun. In June, the Northern Hemisphere “leans into” the Sun, and those in the North experience summer and have longer days. In December, during winter in the Northern Hemisphere, the Southern Hemisphere “leans into” the Sun and is illuminated more directly. In spring and autumn, the two hemispheres receive more equal shares of sunlight. [1] How does the Sun’s favoring one hemisphere translate into making it warmer for us down on the surface of Earth? There are two effects we need to consider. When we lean into the Sun, sunlight hits us at a more direct angle and is more effective at heating Earth’s surface (Figure 4.6). You can get a similar effect by shining a flashlight onto a wall. If you shine the flashlight straight on, you get an intense spot of light on the wall. But if you hold the flashlight at an angle (if the wall “leans out” of the beam), then the spot of light is more spread out. Like the straight-on light, the sunlight in June is more direct and intense in the Northern Hemisphere, and hence more effective at heating. 1 Note that the dates indicated for the solstices and equinoxes are approximate; depending on the year, they may occur a day or two earlier or later. 108 Chapter 4 Earth, Moon, and Sky This OpenStax book is available for free at http://cnx.org/content/col11992/1.13
  17. 17. Figure 4.6 The Sun’s Rays in Summer and Winter. (a) In summer, the Sun appears high in the sky and its rays hit Earth more directly, spreading out less. (b) In winter, the Sun is low in the sky and its rays spread out over a much wider area, becoming less effective at heating the ground. The second effect has to do with the length of time the Sun spends above the horizon (Figure 4.7). Even if you’ve never thought about astronomy before, we’re sure you have observed that the hours of daylight increase in summer and decrease in winter. Let’s see why this happens. Figure 4.7 The Sun’s Path in the Sky for Different Seasons. On June 21, the Sun rises north of east and sets north of west. For observers in the Northern Hemisphere of Earth, the Sun spends about 15 hours above the horizon in the United States, meaning more hours of daylight. On December 21, the Sun rises south of east and sets south of west. It spends 9 hours above the horizon in the United States, which means fewer hours of daylight and more hours of night in northern lands (and a strong need for people to hold celebrations to cheer themselves up). On March 21 and September 21, the Sun spends equal amounts of time above and below the horizon in both hemispheres. As we saw in Observing the Sky: The Birth of Astronomy, an equivalent way to look at our path around the Sun each year is to pretend that the Sun moves around Earth (on a circle called the ecliptic). Because Earth’s axis is tilted, the ecliptic is tilted by about 23.5° relative to the celestial equator (review Figure 2.7). As a result, where we see the Sun in the sky changes as the year wears on. In June, the Sun is north of the celestial equator and spends more time with those who live in the Northern Hemisphere. It rises high in the sky and is above the horizon in the United States for as long as 15 hours. Thus, the Sun not only heats us with more direct rays, but it also has more time to do it each day. (Notice in Figure 4.7 Chapter 4 Earth, Moon, and Sky 109
  18. 18. that the Northern Hemisphere’s gain is the Southern Hemisphere’s loss. There the June Sun is low in the sky, meaning fewer daylight hours. In Chile, for example, June is a colder, darker time of year.) In December, when the Sun is south of the celestial equator, the situation is reversed. Let’s look at what the Sun’s illumination on Earth looks like at some specific dates of the year, when these effects are at their maximum. On or about June 21 (the date we who live in the Northern Hemisphere call the summer solstice or sometimes the first day of summer), the Sun shines down most directly upon the Northern Hemisphere of Earth. It appears about 23° north of the equator, and thus, on that date, it passes through the zenith of places on Earth that are at 23° N latitude. The situation is shown in detail in Figure 4.8. To a person at 23° N (near Hawaii, for example), the Sun is directly overhead at noon. This latitude, where the Sun can appear at the zenith at noon on the first day of summer, is called the Tropic of Cancer. We also see in Figure 4.8 that the Sun’s rays shine down all around the North Pole at the solstice. As Earth turns on its axis, the North Pole is continuously illuminated by the Sun; all places within 23° of the pole have sunshine for 24 hours. The Sun is as far north on this date as it can get; thus, 90° – 23° (or 67° N) is the southernmost latitude where the Sun can be seen for a full 24-hour period (sometimes called the “land of the midnight Sun”). That circle of latitude is called the Arctic Circle. Figure 4.8 Earth on June 21. This is the date of the summer solstice in the Northern Hemisphere. Note that as Earth turns on its axis (the line connecting the North and South Poles), the North Pole is in constant sunlight while the South Pole is veiled in 24 hours of darkness. The Sun is at the zenith for observers on the Tropic of Cancer. Many early cultures scheduled special events around the summer solstice to celebrate the longest days and thank their gods for making the weather warm. This required people to keep track of the lengths of the days and the northward trek of the Sun in order to know the right day for the “party.” (You can do the same thing by watching for several weeks, from the same observation point, where the Sun rises or sets relative to a fixed landmark. In spring, the Sun will rise farther and farther north of east, and set farther and farther north of west, reaching the maximum around the summer solstice.) Now look at the South Pole in Figure 4.8. On June 21, all places within 23° of the South Pole—that is, south of what we call the Antarctic Circle—do not see the Sun at all for 24 hours. The situation is reversed 6 months later, about December 21 (the date of the winter solstice, or the first day of winter in the Northern Hemisphere), as shown in Figure 4.9. Now it is the Arctic Circle that has the 24-hour night and the Antarctic Circle that has the midnight Sun. At latitude 23° S, called the Tropic of Capricorn, the Sun passes through the zenith at noon. Days are longer in the Southern Hemisphere and shorter in the north. In the United States and Southern Europe, there may be only 9 or 10 hours of sunshine during the day. It is winter in the Northern Hemisphere and summer in the Southern Hemisphere. 110 Chapter 4 Earth, Moon, and Sky This OpenStax book is available for free at http://cnx.org/content/col11992/1.13
  19. 19. Figure 4.9 Earth on December 21. This is the date of the winter solstice in the Northern Hemisphere. Now the North Pole is in darkness for 24 hours and the South Pole is illuminated. The Sun is at the zenith for observers on the Tropic of Capricorn and thus is low in the sky for the residents of the Northern Hemisphere. E X A M P L E 4 . 1 Seasonal Variations As you can see in Figure 4.8, the Tropic of Cancer is the latitude for which the Sun is directly overhead on the summer solstice. At this time, the Sun is at a declination of 23° N of the celestial equator, and the corresponding latitude on Earth is 23° N of the equator. If Earth were tilted a bit less, then the Tropic of Cancer would be at a lower latitude, closer to the equator. The Arctic Circle marks the southernmost latitude for which the day length is 24 hours on the day of the summer solstice. This is located at 90° – 23° = 67° N of Earth’s equator. If Earth were tilted a bit less, then the Arctic Circle would move farther North. In the limit at which Earth is not tilted at all (its axis is perpendicular to the ecliptic), the Tropic of Cancer would be right on Earth’s equator, and the Arctic Circle would simply be the North Pole. Suppose the tilt of Earth’s axis were tilted only 5°. What would be the effect on the seasons and the locations of the Tropic of Cancer and Arctic Circle? Solution If Earth were tilted less, the seasons would be less extreme. The variation in day length and direct sunlight would be very small over the course of a year, and the Sun’s daily path in the sky would not vary much. If Earth were tilted by 5°, the Sun’s position on the day of the summer solstice would be 5° N of the celestial equator, so the Tropic of Cancer would be at the corresponding latitude on Earth of 5° N of the Equator. The Arctic Circle would be located at 90° – 5° = 85° N of the equator. Check Your Learning Suppose the tilt of Earth’s axis were 16°. What, then, would be the difference in latitude between the Arctic Circle and the Tropic of Cancer? What would be the effect on the seasons compared with that produced by the actual tilt of 23°? Answer: The Tropic of Cancer is at a latitude equal to Earth’s tilt, so in this case, it would be at 16° N latitude. The Chapter 4 Earth, Moon, and Sky 111
  20. 20. Many cultures that developed some distance north of the equator have a celebration around December 21 to help people deal with the depressing lack of sunlight and the often dangerously cold temperatures. Originally, this was often a time for huddling with family and friends, for sharing the reserves of food and drink, and for rituals asking the gods to return the light and heat and turn the cycle of the seasons around. Many cultures constructed elaborate devices for anticipating when the shortest day of the year was coming. Stonehenge in England, built long before the invention of writing, is probably one such device. In our own time, we continue the winter solstice tradition with various holiday celebrations around that December date. Halfway between the solstices, on about March 21 and September 21, the Sun is on the celestial equator. From Earth, it appears above our planet’s equator and favors neither hemisphere. Every place on Earth then receives roughly 12 hours of sunshine and 12 hours of night. The points where the Sun crosses the celestial equator are called the vernal (spring) and autumnal (fall) equinoxes. The Seasons at Different Latitudes The seasonal effects are different at different latitudes on Earth. Near the equator, for instance, all seasons are much the same. Every day of the year, the Sun is up half the time, so there are approximately 12 hours of sunshine and 12 hours of night. Local residents define the seasons by the amount of rain (wet season and dry season) rather than by the amount of sunlight. As we travel north or south, the seasons become more pronounced, until we reach extreme cases in the Arctic and Antarctic. At the North Pole, all celestial objects that are north of the celestial equator are always above the horizon and, as Earth turns, circle around parallel to it. The Sun is north of the celestial equator from about March 21 to September 21, so at the North Pole, the Sun rises when it reaches the vernal equinox and sets when it reaches the autumnal equinox. Each year there are 6 months of sunshine at each pole, followed by 6 months of darkness. Arctic Circle is at a latitude equal to 90° minus Earth’s tilt, or 90° – 16° = 74°. The difference between these two latitudes is 74° – 16° = 58°. Since the tilt of Earth is less, there would be less variation in the tilt of Earth and less variation in the Sun’s paths throughout the year, so there would be milder seasonal changes. L I N K T O L E A R N I N G You can see an animation (https://openstaxcollege.org/l/30anisunpath) of the Sun’s path during the seasons alongside a time-lapse view of light and shadow from a camera set up on the University of Nebraska campus. E X A M P L E 4 . 2 The Position of the Sun in the Sky 112 Chapter 4 Earth, Moon, and Sky This OpenStax book is available for free at http://cnx.org/content/col11992/1.13
  21. 21. Clarifications about the Real World In our discussions so far, we have been describing the rising and setting of the Sun and stars as they would appear if Earth had little or no atmosphere. In reality, however, the atmosphere has the curious effect of allowing us to see a little way “over the horizon.” This effect is a result of refraction, the bending of light passing through air or water, something we will discuss in Astronomical Instruments. Because of this atmospheric refraction (and the fact that the Sun is not a point of light but a disk), the Sun appears to rise earlier and to set later than it would if no atmosphere were present. In addition, the atmosphere scatters light and provides some twilight illumination even when the Sun is below the horizon. Astronomers define morning twilight as beginning when the Sun is 18° below the horizon, and evening twilight extends until the Sun sinks more than 18° below the horizon. These atmospheric effects require small corrections in many of our statements about the seasons. At the equinoxes, for example, the Sun appears to be above the horizon for a few minutes longer than 12 hours, and below the horizon for fewer than 12 hours. These effects are most dramatic at Earth’s poles, where the Sun actually can be seen more than a week before it reaches the celestial equator. You probably know that the summer solstice (June 21) is not the warmest day of the year, even if it is the longest. The hottest months in the Northern Hemisphere are July and August. This is because our weather involves the air and water covering Earth’s surface, and these large reservoirs do not heat up instantaneously. You have probably observed this effect for yourself; for example, a pond does not get warm the moment the Sun rises but is warmest late in the afternoon, after it has had time to absorb the Sun’s heat. In the same way, Earth gets warmer after it has had a chance to absorb the extra sunlight that is the Sun’s summer gift to us. And the coldest times of winter are a month or more after the winter solstice. The Sun’s coordinates on the celestial sphere range from a declination of 23° N of the celestial equator (or +23°) to a declination 23° S of the celestial equator (or –23°). So, the Sun’s altitude at noon, when it crosses the meridian, varies by a total of 46°. What is the altitude of the Sun at noon on March 21, as seen from a place on Earth’s equator? What is its altitude on June 21, as seen from a place on Earth’s equator? Solution On Earth’s equator, the celestial equator passes through the zenith. On March 21, the Sun is crossing the celestial equator, so it should be found at the zenith (90°) at noon. On June 21, the Sun is 23° N of the celestial equator, so it will be 23° away from the zenith at noon. The altitude above the horizon will be 23° less than the altitude of the zenith (90°), so it is 90° – 23° = 67° above the horizon. Check Your Learning What is the altitude of the Sun at noon on December 21, as seen from a place on the Tropic of Cancer? Answer: On the day of the winter solstice, the Sun is located about 23° S of the celestial equator. From the Tropic of Cancer, a latitude of 23° N, the zenith would be a declination of 23° N. The difference in declination between zenith and the position of the Sun is 46°, so the Sun would be 46° away from the zenith. That means it would be at an altitude of 90° – 46° = 44°. Chapter 4 Earth, Moon, and Sky 113
  22. 22. 4.3 KEEPING TIME Learning Objectives By the end of this section, you will be able to: Explain the difference between the solar day and the sidereal day Explain mean solar time and the reason for time zones The measurement of time is based on the rotation of Earth. Throughout most of human history, time has been reckoned by positions of the Sun and stars in the sky. Only recently have mechanical and electronic clocks taken over this function in regulating our lives. The Length of the Day The most fundamental astronomical unit of time is the day, measured in terms of the rotation of Earth. There is, however, more than one way to define the day. Usually, we think of it as the rotation period of Earth with respect to the Sun, called the solar day. After all, for most people sunrise is more important than the rising time of Arcturus or some other star, so we set our clocks to some version of Sun-time. However, astronomers also use a sidereal day, which is defined in terms of the rotation period of Earth with respect to the stars. A solar day is slightly longer than a sidereal day because (as you can see from Figure 4.10) Earth not only turns but also moves along its path around the Sun in a day. Suppose we start when Earth’s orbital position is at day 1, with both the Sun and some distant star (located in the direction indicated by the long white arrow pointing left), directly in line with the zenith for the observer on Earth. When Earth has completed one rotation with respect to the distant star and is at day 2, the long arrow again points to the same distant star. However, notice that because of the movement of Earth along its orbit from day 1 to 2, the Sun has not yet reached a position above the observer. To complete a solar day, Earth must rotate an additional amount, equal to 1/365 of a full turn. The time required for this extra rotation is 1/365 of a day, or about 4 minutes. So the solar day is about 4 minutes longer than the sidereal day. Figure 4.10 Difference Between a Sidereal Day and a Solar Day. This is a top view, looking down as Earth orbits the Sun. Because Earth moves around the Sun (roughly 1° per day), after one complete rotation of Earth relative to the stars, we do not see the Sun in the same position. Because our ordinary clocks are set to solar time, stars rise 4 minutes earlier each day. Astronomers prefer sidereal time for planning their observations because in that system, a star rises at the same time every day. 114 Chapter 4 Earth, Moon, and Sky This OpenStax book is available for free at http://cnx.org/content/col11992/1.13
  23. 23. Apparent Solar Time We can define apparent solar time as time reckoned by the actual position of the Sun in the sky (or, during the night, its position below the horizon). This is the kind of time indicated by sundials, and it probably represents the earliest measure of time used by ancient civilizations. Today, we adopt the middle of the night as the starting point of the day and measure time in hours elapsed since midnight. During the first half of the day, the Sun has not yet reached the meridian (the great circle in the sky that passes through our zenith). We designate those hours as before midday (ante meridiem, or a.m.), before the Sun reaches the local meridian. We customarily start numbering the hours after noon over again and designate them by p.m. (post meridiem), after the Sun reaches the local meridian. Although apparent solar time seems simple, it is not really very convenient to use. The exact length of an apparent solar day varies slightly during the year. The eastward progress of the Sun in its annual journey around the sky is not uniform because the speed of Earth varies slightly in its elliptical orbit. Another complication is that Earth’s axis of rotation is not perpendicular to the plane of its revolution. Thus, apparent E X A M P L E 4 . 3 Sidereal Time and Solar Time The Sun makes a complete circle in the sky approximately every 24 hours, while the stars make a complete circle in the sky in 4 minutes less time, or 23 hours and 56 minutes. This causes the positions of the stars at a given time of day or night to change slightly each day. Since stars rise 4 minutes earlier each day, that works out to about 2 hours per month (4 minutes × 30 = 120 minutes or 2 hours). So, if a particular constellation rises at sunset during the winter, you can be sure that by the summer, it will rise about 12 hours earlier, with the sunrise, and it will not be so easily visible in the night sky. Let’s say that tonight the bright star Sirius rises at 7:00 p.m. from a given location so that by midnight, it is very high in the sky. At what time will Sirius rise in three months? Solution In three months’ time, Sirius will be rising earlier by: 90 days × 4 minutes day = 360 minutes or 6 hours It will rise at about 1:00 p.m. and be high in the sky at around sunset instead of midnight. Sirius is the brightest star in the constellation of Canis Major (the big dog). So, some other constellation will be prominently visible high in the sky at this later date. Check Your Learning If a star rises at 8:30 p.m. tonight, approximately what time will it rise two months from now? Answer: In two months, the star will rise: 60 days × 4 minutes day = 240 minutes or 4 hours earlier. This means it will rise at 4:30 p.m. Chapter 4 Earth, Moon, and Sky 115
  24. 24. solar time does not advance at a uniform rate. After the invention of mechanical clocks that run at a uniform rate, it became necessary to abandon the apparent solar day as the fundamental unit of time. Mean Solar Time and Standard Time Instead, we can consider the mean solar time, which is based on the average value of the solar day over the course of the year. A mean solar day contains exactly 24 hours and is what we use in our everyday timekeeping. Although mean solar time has the advantage of progressing at a uniform rate, it is still inconvenient for practical use because it is determined by the position of the Sun. For example, noon occurs when the Sun is highest in the sky on the meridian (but not necessarily at the zenith). But because we live on a round Earth, the exact time of noon is different as you change your longitude by moving east or west. If mean solar time were strictly observed, people traveling east or west would have to reset their watches continually as the longitude changed, just to read the local mean time correctly. For instance, a commuter traveling from Oyster Bay on Long Island to New York City would have to adjust the time on the trip through the East River tunnel because Oyster Bay time is actually about 1.6 minutes more advanced than that of Manhattan. (Imagine an airplane trip in which an obnoxious flight attendant gets on the intercom every minute, saying, “Please reset your watch for local mean time.”) Until near the end of the nineteenth century, every city and town in the United States kept its own local mean time. With the development of railroads and the telegraph, however, the need for some kind of standardization became evident. In 1883, the United States was divided into four standard time zones (now six, including Hawaii and Alaska), each with one system of time within that zone. By 1900, most of the world was using the system of 24 standardized global time zones. Within each zone, all places keep the same standard time, with the local mean solar time of a standard line of longitude running more or less through the middle of each zone. Now travelers reset their watches only when the time change has amounted to a full hour. Pacific standard time is 3 hours earlier than eastern standard time, a fact that becomes painfully obvious in California when someone on the East Coast forgets and calls you at 5:00 a.m. Globally, almost all countries have adopted one or more standard time zones, although one of the largest nations, India, has settled on a half-zone, being 5.5 hours from Greenwich standard. Also, China officially uses only one time zone, so all the clocks in that country keep the same time. In Tibet, for example, the Sun rises while the clocks (which keep Beijing time) say it is midmorning already. Daylight saving time is simply the local standard time of the place plus 1 hour. It has been adopted for spring and summer use in most states in the United States, as well as in many countries, to prolong the sunlight into evening hours, on the apparent theory that it is easier to change the time by government action than it would be for individuals or businesses to adjust their own schedules to produce the same effect. It does not, of course, “save” any daylight at all—because the amount of sunlight is not determined by what we do with our clocks—and its observance is a point of legislative debate in some states. The International Date Line The fact that time is always advancing as you move toward the east presents a problem. Suppose you travel eastward around the world. You pass into a new time zone, on the average, about every 15° of longitude you travel, and each time you dutifully set your watch ahead an hour. By the time you have completed your trip, you have set your watch ahead a full 24 hours and thus gained a day over those who stayed at home. The solution to this dilemma is the International Date Line, set by international agreement to run approximately along the 180° meridian of longitude. The date line runs down the middle of the Pacific Ocean, although it jogs a bit in a few places to avoid cutting through groups of islands and through Alaska (Figure 116 Chapter 4 Earth, Moon, and Sky This OpenStax book is available for free at http://cnx.org/content/col11992/1.13
  25. 25. 4.11). By convention, at the date line, the date of the calendar is changed by one day. Crossing the date line from west to east, thus advancing your time, you compensate by decreasing the date; crossing from east to west, you increase the date by one day. To maintain our planet on a rational system of timekeeping, we simply must accept that the date will differ in different cities at the same time. A good example is the date when the Imperial Japanese Navy bombed Pearl Harbor in Hawaii, known in the United States as Sunday, December 7, 1941, but taught to Japanese students as Monday, December 8. Figure 4.11 Where the Date Changes. The International Date Line is an arbitrarily drawn line on Earth where the date changes. So that neighbors do not have different days, the line is located where Earth’s surface is mostly water. 4.4 THE CALENDAR Learning Objectives By the end of this section, you will be able to: Understand how calendars varied among different cultures Explain the origins of our modern calendar “What’s today’s date?” is one of the most common questions you can ask (usually when signing a document or worrying about whether you should have started studying for your next astronomy exam). Long before the era of digital watches, smartphones, and fitness bands that tell the date, people used calendars to help measure the passage of time. The Challenge of the Calendar There are two traditional functions of any calendar. First, it must keep track of time over the course of long spans, allowing people to anticipate the cycle of the seasons and to honor special religious or personal anniversaries. Second, to be useful to a large number of people, a calendar must use natural time intervals that everyone can agree on—those defined by the motions of Earth, the Moon, and sometimes even the planets. The natural units of our calendar are the day, based on the period of rotation of Earth; the month, based on the cycle of the Moon’s phases (see later in this chapter) about Earth; and the year, based on the period of revolution of Earth about the Sun. Difficulties have resulted from the fact that these three periods are not commensurable; that’s a fancy way of saying that one does not divide evenly into any of the others. The rotation period of Earth is, by definition, 1.0000 day (and here the solar day is used, since that is the basis of human experience). The period required by the Moon to complete its cycle of phases, called the month, is Chapter 4 Earth, Moon, and Sky 117
  26. 26. 29.5306 days. The basic period of revolution of Earth, called the tropical year, is 365.2422 days. The ratios of these numbers are not convenient for calculations. This is the historic challenge of the calendar, dealt with in various ways by different cultures. Early Calendars Even the earliest cultures were concerned with the keeping of time and the calendar. Some interesting examples include monuments left by Bronze Age people in northwestern Europe, especially the British Isles. The best preserved of the monuments is Stonehenge, about 13 kilometers from Salisbury in southwest England (Figure 4.12). It is a complex array of stones, ditches, and holes arranged in concentric circles. Carbon dating and other studies show that Stonehenge was built during three periods ranging from about 2800 to 1500 BCE. Some of the stones are aligned with the directions of the Sun and Moon during their risings and settings at critical times of the year (such as the summer and winter solstices), and it is generally believed that at least one function of the monument was connected with the keeping of a calendar. Figure 4.12 Stonehenge. The ancient monument known as Stonehenge was used to keep track of the motions of the Sun and Moon. (credit: modification of work by Adriano Aurelio Araujo) The Maya in Central America, who thrived more than a thousand years ago, were also concerned with the keeping of time. Their calendar was as sophisticated as, and perhaps more complex than, contemporary calendars in Europe. The Maya did not attempt to correlate their calendar accurately with the length of the year or lunar month. Rather, their calendar was a system for keeping track of the passage of days and for counting time far into the past or future. Among other purposes, it was useful for predicting astronomical events, such as the position of Venus in the sky (Figure 4.13). 118 Chapter 4 Earth, Moon, and Sky This OpenStax book is available for free at http://cnx.org/content/col11992/1.13
  27. 27. Figure 4.13 El Caracol. This Mayan observatory at Chichen Itza in the Yucatan, Mexico, dates from around the year 1000. (credit: “wiredtourist.com”/Flickr) The ancient Chinese developed an especially complex calendar, largely limited to a few privileged hereditary court astronomer-astrologers. In addition to the motions of Earth and the Moon, they were able to fit in the approximately 12-year cycle of Jupiter, which was central to their system of astrology. The Chinese still preserve some aspects of this system in their cycle of 12 “years”—the Year of the Dragon, the Year of the Pig, and so on—that are defined by the position of Jupiter in the zodiac. Our Western calendar derives from a long history of timekeeping beginning with the Sumerians, dating back to at least the second millennium BCE, and continuing with the Egyptians and the Greeks around the eighth century BCE. These calendars led, eventually, to the Julian calendar, introduced by Julius Caesar, which approximated the year at 365.25 days, fairly close to the actual value of 365.2422. The Romans achieved this approximation by declaring years to have 365 days each, with the exception of every fourth year. The leap year was to have one extra day, bringing its length to 366 days, and thus making the average length of the year in the Julian calendar 365.25 days. In this calendar, the Romans had dropped the almost impossible task of trying to base their calendar on the Moon as well as the Sun, although a vestige of older lunar systems can be seen in the fact that our months have an average length of about 30 days. However, lunar calendars remained in use in other cultures, and Islamic calendars, for example, are still primarily lunar rather than solar. The Gregorian Calendar Although the Julian calendar (which was adopted by the early Christian Church) represented a great advance, its average year still differed from the true year by about 11 minutes, an amount that accumulates over the centuries to an appreciable error. By 1582, that 11 minutes per year had added up to the point where the first day of spring was occurring on March 11, instead of March 21. If the trend were allowed to continue, eventually the Christian celebration of Easter would be occurring in early winter. Pope Gregory XIII, a contemporary of Galileo, felt it necessary to institute further calendar reform. The Gregorian calendar reform consisted of two steps. First, 10 days had to be dropped out of the calendar to bring the vernal equinox back to March 21; by proclamation, the day following October 4, 1582, became October 15. The second feature of the new Gregorian calendar was a change in the rule for leap year, making the average length of the year more closely approximate the tropical year. Gregory decreed that three of every four century years—all leap years under the Julian calendar—would be common years henceforth. The rule was that only century years divisible by 400 would be leap years. Thus, 1700, 1800, and 1900—all divisible by 4 but not by 400—were not leap years in the Gregorian calendar. On the other hand, the years 1600 and 2000, both Chapter 4 Earth, Moon, and Sky 119
  28. 28. divisible by 400, were leap years. The average length of this Gregorian year, 365.2425 mean solar days, is correct to about 1 day in 3300 years. The Catholic countries immediately put the Gregorian reform into effect, but countries of the Eastern Church and most Protestant countries did not adopt it until much later. It was 1752 when England and the American colonies finally made the change. By parliamentary decree, September 2, 1752, was followed by September 14. Although special laws were passed to prevent such abuses as landlords collecting a full month’s rent for September, there were still riots, and people demanded their 12 days back. Russia did not abandon the Julian calendar until the time of the Bolshevik revolution. The Russians then had to omit 13 days to come into step with the rest of the world. The anniversary of the October Revolution (old calendar) of 1917, bringing the communists to power, thus ended up being celebrated in November (new calendar), a difference that is perhaps not so important since the fall of communism. 4.5 PHASES AND MOTIONS OF THE MOON Learning Objectives By the end of this section, you will be able to: Explain the cause of the lunar phases Understand how the Moon rotates and revolves around Earth After the Sun, the Moon is the brightest and most obvious object in the sky. Unlike the Sun, it does not shine under its own power, but merely glows with reflected sunlight. If you were to follow its progress in the sky for a month, you would observe a cycle of phases (different appearances), with the Moon starting dark and getting more and more illuminated by sunlight over the course of about two weeks. After the Moon’s disk becomes fully bright, it begins to fade, returning to dark about two weeks later. These changes fascinated and mystified many early cultures, which came up with marvelous stories and legends to explain the cycle of the Moon. Even in the modern world, many people don’t understand what causes the phases, thinking that they are somehow related to the shadow of Earth. Let us see how the phases can be explained by the motion of the Moon relative to the bright light source in the solar system, the Sun. Lunar Phases Although we know that the Sun moves 1/12 of its path around the sky each month, for purposes of explaining the phases, we can assume that the Sun’s light comes from roughly the same direction during the course of a four-week lunar cycle. The Moon, on the other hand, moves completely around Earth in that time. As we watch the Moon from our vantage point on Earth, how much of its face we see illuminated by sunlight depends on the angle the Sun makes with the Moon. Here is a simple experiment to show you what we mean: stand about 6 feet in front of a bright electric light in a completely dark room (or outdoors at night) and hold in your hand a small round object such as a tennis ball or an orange. Your head can then represent Earth, the light represents the Sun, and the ball the Moon. Move the ball around your head (making sure you don’t cause an eclipse by blocking the light with your head). You will see phases just like those of the Moon on the ball. (Another good way to get acquainted with the phases and motions of the Moon is to follow our satellite in the sky for a month or two, recording its shape, its direction from the Sun, and when it rises and sets.) Let’s examine the Moon’s cycle of phases using Figure 4.14, which depicts the Moon’s behavior for the entire month. The trick to this figure is that you must imagine yourself standing on Earth, facing the Moon in each of 120 Chapter 4 Earth, Moon, and Sky This OpenStax book is available for free at http://cnx.org/content/col11992/1.13
  29. 29. its phases. So, for the position labeled “New,” you are on the right side of Earth and it’s the middle of the day; for the position “Full,” you are on the left side of Earth in the middle of the night. Note that in every position on Figure 4.14, the Moon is half illuminated and half dark (as a ball in sunlight should be). The difference at each position has to do with what part of the Moon faces Earth. Figure 4.14 Phases of the Moon. The appearance of the Moon changes over the course of a complete monthly cycle. The pictures of the Moon on the white circle show the perspective from space, with the Sun off to the right in a fixed position. The outer images show how the Moon appears to you in the sky from each point in the orbit. Imagine yourself standing on Earth, facing the Moon at each stage. In the position “New,” for example, you are facing the Moon from the right side of Earth in the middle of the day. (Note that the distance of the Moon from Earth is not to scale in this diagram: the Moon is roughly 30 Earth-diameters away from us.) (credit: modification of work by NASA) The Moon is said to be new when it is in the same general direction in the sky as the Sun (position A). Here, its illuminated (bright) side is turned away from us and its dark side is turned toward us. You might say that the Sun is shining on the “wrong ” side of the Moon from our perspective. In this phase the Moon is invisible to us; its dark, rocky surface does not give off any light of its own. Because the new moon is in the same part of the sky as the Sun, it rises at sunrise and sets at sunset. But the Moon does not remain in this phase long because it moves eastward each day in its monthly path around us. Since it takes about 30 days to orbit Earth and there are 360° in a circle, the Moon will move about 12° in the sky each day (or about 24 times its own diameter). A day or two after the new phase, the thin crescent first appears, as we begin to see a small part of the Moon’s illuminated hemisphere. It has moved into a position where it now reflects a little sunlight toward us along one side. The bright crescent increases in size on successive days as the Moon moves farther and farther around the sky away from the direction of the Sun (position B). Because the Moon is moving eastward away from the Sun, it rises later and later each day (like a student during summer vacation). After about one week, the Moon is one-quarter of the way around its orbit (position C) and so we say it is at the first quarter phase. Half of the Moon’s illuminated side is visible to Earth observers. Because of its eastward motion, the Moon now lags about one-quarter of the day behind the Sun, rising around noon and setting around midnight. During the week after the first quarter phase, we see more and more of the Moon’s illuminated hemisphere (position D), a phase that is called waxing (or growing) gibbous (from the Latin gibbus, meaning hump). Eventually, the Moon arrives at position E in our figure, where it and the Sun are opposite each other in the sky. Chapter 4 Earth, Moon, and Sky 121
  30. 30. The side of the Moon turned toward the Sun is also turned toward Earth, and we have the full phase. When the Moon is full, it is opposite the Sun in the sky. The Moon does the opposite of what the Sun does, rising at sunset and setting at sunrise. Note what that means in practice: the completely illuminated (and thus very noticeable) Moon rises just as it gets dark, remains in the sky all night long, and sets as the Sun’s first rays are seen at dawn. Its illumination throughout the night helps lovers on a romantic stroll and students finding their way back to their dorms after a long night in the library or an off-campus party. And when is the full moon highest in the sky and most noticeable? At midnight, a time made famous in generations of horror novels and films. (Note how the behavior of a vampire like Dracula parallels the behavior of the full Moon: Dracula rises at sunset, does his worst mischief at midnight, and must be back down in his coffin by sunrise. The old legends were a way of personifying the behavior of the Moon, which was a much more dramatic part of people’s lives in the days before electric lights and television.) Folklore has it that more crazy behavior is seen during the time of the full moon (the Moon even gives a name to crazy behavior—“lunacy”). But, in fact, statistical tests of this “hypothesis” involving thousands of records from hospital emergency rooms and police files do not reveal any correlation of human behavior with the phases of the Moon. For example, homicides occur at the same rate during the new moon or the crescent moon as during the full moon. Most investigators believe that the real story is not that more crazy behavior happens on nights with a full moon, but rather that we are more likely to notice or remember such behavior with the aid of a bright celestial light that is up all night long. During the two weeks following the full moon, the Moon goes through the same phases again in reverse order (points F, G, and H in Figure 4.14), returning to new phase after about 29.5 days. About a week after the full moon, for example, the Moon is at third quarter, meaning that it is three-quarters of the way around (not that it is three-quarters illuminated—in fact, half of the visible side of the Moon is again dark). At this phase, the Moon is now rising around midnight and setting around noon. Note that there is one thing quite misleading about Figure 4.14. If you look at the Moon in position E, although it is full in theory, it appears as if its illumination would in fact be blocked by a big fat Earth, and hence we would not see anything on the Moon except Earth’s shadow. In reality, the Moon is nowhere near as close to Earth (nor is its path so identical with the Sun’s in the sky) as this diagram (and the diagrams in most textbooks) might lead you to believe. The Moon is actually 30 Earth-diameters away from us; Science and the Universe: A Brief Tour contains a diagram that shows the two objects to scale. And, since the Moon’s orbit is tilted relative to the path of the Sun in the sky, Earth’s shadow misses the Moon most months. That’s why we regularly get treated to a full moon. The times when Earth’s shadow does fall on the Moon are called lunar eclipses and are discussed in Eclipses of the Sun and Moon. M A K I N G C O N N E C T I O N S Astronomy and the Days of the Week The week seems independent of celestial motions, although its length may have been based on the time between quarter phases of the Moon. In Western culture, the seven days of the week are named after the seven “wanderers” that the ancients saw in the sky: the Sun, the Moon, and the five planets visible to the unaided eye (Mercury, Venus, Mars, Jupiter, and Saturn). 122 Chapter 4 Earth, Moon, and Sky This OpenStax book is available for free at http://cnx.org/content/col11992/1.13
  31. 31. The Moon’s Revolution and Rotation The Moon’s sidereal period—that is, the period of its revolution about Earth measured with respect to the stars—is a little over 27 days: the sidereal month is 27.3217 days to be exact. The time interval in which the phases repeat—say, from full to full—is the solar month, 29.5306 days. The difference results from Earth’s motion around the Sun. The Moon must make more than a complete turn around the moving Earth to get back to the same phase with respect to the Sun. As we saw, the Moon changes its position on the celestial sphere rather rapidly: even during a single evening, the Moon creeps visibly eastward among the stars, traveling its own width in a little less than 1 hour. The delay in moonrise from one day to the next caused by this eastward motion averages about 50 minutes. The Moon rotates on its axis in exactly the same time that it takes to revolve about Earth. As a consequence, the Moon always keeps the same face turned toward Earth (Figure 4.15). You can simulate this yourself by “orbiting” your roommate or another volunteer. Start by facing your roommate. If you make one rotation (spin) with your shoulders in the exact same time that you revolve around him or her, you will continue to face your roommate during the whole “orbit.” As we will see in coming chapters, our Moon is not the only world that exhibits this behavior, which scientists call synchronous rotation. In English, we can easily recognize the names Sun-day (Sunday), Moon-day (Monday), and Saturn-day (Saturday), but the other days are named after the Norse equivalents of the Roman gods that gave their names to the planets. In languages more directly related to Latin, the correspondences are clearer. Wednesday, Mercury’s day, for example, is mercoledi in Italian, mercredi in French, and miércoles in Spanish. Mars gives its name to Tuesday (martes in Spanish), Jupiter or Jove to Thursday (giovedi in Italian), and Venus to Friday (vendredi in French). There is no reason that the week has to have seven days rather than five or eight. It is interesting to speculate that if we had lived in a planetary system where more planets were visible without a telescope, the Beatles could have been right and we might well have had “Eight Days a Week.” L I N K T O L E A R N I N G View this animation (https://openstaxcollege.org/l/30phamoonearth) to see the phases of the Moon as it orbits Earth and as Earth orbits the Sun. Chapter 4 Earth, Moon, and Sky 123
  32. 32. Figure 4.15 The Moon without and with Rotation. In this figure, we stuck a white arrow into a fixed point on the Moon to keep track of its sides. (a) If the Moon did not rotate as it orbited Earth, it would present all of its sides to our view; hence the white arrow would point directly toward Earth only in the bottom position on the diagram. (b) Actually, the Moon rotates in the same period that it revolves, so we always see the same side (the white arrow keeps pointing to Earth). The differences in the Moon’s appearance from one night to the next are due to changing illumination by the Sun, not to its own rotation. You sometimes hear the back side of the Moon (the side we never see) called the “dark side.” This is a misunderstanding of the real situation: which side is light and which is dark changes as the Moon moves around Earth. The back side is dark no more frequently than the front side. Since the Moon rotates, the Sun rises and sets on all sides of the Moon. With apologies to Pink Floyd, there is simply no regular “Dark Side of the Moon.” 124 Chapter 4 Earth, Moon, and Sky This OpenStax book is available for free at http://cnx.org/content/col11992/1.13
  33. 33. 4.6 OCEAN TIDES AND THE MOON Learning Objectives By the end of this section, you will be able to: Describe what causes tides on Earth Explain why the amplitude of tides changes during the course of a month Anyone living near the sea is familiar with the twice-daily rising and falling of the tides. Early in history, it was clear that tides must be related to the Moon because the daily delay in high tide is the same as the daily delay in the Moon’s rising. A satisfactory explanation of the tides, however, awaited the theory of gravity, supplied by Newton. The Pull of the Moon on Earth The gravitational forces exerted by the Moon at several points on Earth are illustrated in Figure 4.16. These forces differ slightly from one another because Earth is not a point, but has a certain size: all parts are not equally distant from the Moon, nor are they all in exactly the same direction from the Moon. Moreover, Earth is not perfectly rigid. As a result, the differences among the forces of the Moon’s attraction on different parts of Earth (called differential forces) cause Earth to distort slightly. The side of Earth nearest the Moon is attracted toward the Moon more strongly than is the center of Earth, which in turn is attracted more strongly than is the side opposite the Moon. Thus, the differential forces tend to stretch Earth slightly into a prolate spheroid (a football shape), with its long diameter pointed toward the Moon. Figure 4.16 Pull of the Moon. The Moon’s differential attraction is shown on different parts of Earth. (Note that the differences have been exaggerated for educational purposes.) If Earth were made of water, it would distort until the Moon’s differential forces over different parts of its surface came into balance with Earth’s own gravitational forces pulling it together. Calculations show that in this case, Earth would distort from a sphere by amounts ranging up to nearly 1 meter. Measurements of the actual deformation of Earth show that the solid Earth does distort, but only about one-third as much as water would, because of the greater rigidity of Earth’s interior. Because the tidal distortion of the solid Earth amounts—at its greatest—to only about 20 centimeters, Earth does not distort enough to balance the Moon’s differential forces with its own gravity. Hence, objects at Earth’s surface experience tiny horizontal tugs, tending to make them slide about. These tide-raising forces are too insignificant to affect solid objects like astronomy students or rocks in Earth’s crust, but they do affect the Chapter 4 Earth, Moon, and Sky 125
  34. 34. waters in the oceans. The Formation of Tides The tide-raising forces, acting over a number of hours, produce motions of the water that result in measurable tidal bulges in the oceans. Water on the side of Earth facing the Moon flows toward it, with the greatest depths roughly at the point below the Moon. On the side of Earth opposite the Moon, water also flows to produce a tidal bulge (Figure 4.17). Figure 4.17 Tidal Bulges in an “Ideal” Ocean. Differences in gravity cause tidal forces that push water in the direction of tidal bulges on Earth. Note that the tidal bulges in the oceans do not result from the Moon’s compressing or expanding the water, nor from the Moon’s lifting the water “away from Earth.” Rather, they result from an actual flow of water over Earth’s surface toward the two regions below and opposite the Moon, causing the water to pile up to greater depths at those places (Figure 4.18). Figure 4.18 High and Low Tides. This is a side-by-side comparison of the Bay of Fundy in Canada at high and low tides. (credit a, b: modification of work by Dylan Kereluk) In the idealized (and, as we shall see, oversimplified) model just described, the height of the tides would be only L I N K T O L E A R N I N G You can run this animation (https://openstaxcollege.org/l/30visdemotidal) for a visual demonstration of the tidal bulge. 126 Chapter 4 Earth, Moon, and Sky This OpenStax book is available for free at http://cnx.org/content/col11992/1.13
  35. 35. a few feet. The rotation of Earth would carry an observer at any given place alternately into regions of deeper and shallower water. An observer being carried toward the regions under or opposite the Moon, where the water was deepest, would say, “The tide is coming in”; when carried away from those regions, the observer would say, “The tide is going out.” During a day, the observer would be carried through two tidal bulges (one on each side of Earth) and so would experience two high tides and two low tides. The Sun also produces tides on Earth, although it is less than half as effective as the Moon at tide raising. The actual tides we experience are a combination of the larger effect of the Moon and the smaller effect of the Sun. When the Sun and Moon are lined up (at new moon or full moon), the tides produced reinforce each other and so are greater than normal (Figure 4.19). These are called spring tides (the name is connected not to the season but to the idea that higher tides “spring up”). Spring tides are approximately the same, whether the Sun and Moon are on the same or opposite sides of Earth, because tidal bulges occur on both sides. When the Moon is at first quarter or last quarter (at right angles to the Sun’s direction), the tides produced by the Sun partially cancel the tides of the Moon, making them lower than usual. These are called neap tides. Figure 4.19 Tides Caused by Different Alignments of the Sun and Moon. (a) In spring tides, the Sun’s and Moon’s pulls reinforce each other. (b) In neap tides, the Sun and the Moon pull at right angles to each other and the resulting tides are lower than usual. The “simple” theory of tides, described in the preceding paragraphs, would be sufficient if Earth rotated very slowly and were completely surrounded by very deep oceans. However, the presence of land masses stopping the flow of water, the friction in the oceans and between oceans and the ocean floors, the rotation of Earth, the wind, the variable depth of the ocean, and other factors all complicate the picture. This is why, in the real world, some places have very small tides while in other places huge tides become tourist attractions. If you have been in such places, you may know that “tide tables” need to be computed and published for each location; one set of tide predictions doesn’t work for the whole planet. In this introductory chapter, we won’t delve further into these complexities. V O YA G E R S I N A S T R O N O M Y George Darwin and the Slowing of Earth The rubbing of water over the face of Earth involves an enormous amount of energy. Over long periods Chapter 4 Earth, Moon, and Sky 127
  36. 36. of time, the friction of the tides is slowing down the rotation of Earth. Our day gets longer by about 0.002 second each century. That seems very small, but such tiny changes can add up over millions and billions of years. Although Earth’s spin is slowing down, the angular momentum (see Orbits and Gravity) in a system such as the Earth-Moon system cannot change. Thus, some other spin motion must speed up to take the extra angular momentum. The details of what happens were worked out over a century ago by George Darwin, the son of naturalist Charles Darwin. George Darwin (see Figure 4.20) had a strong interest in science but studied law for six years and was admitted to the bar. However, he never practiced law, returning to science instead and eventually becoming a professor at Cambridge University. He was a protégé of Lord Kelvin, one of the great physicists of the nineteenth century, and he became interested in the long-term evolution of the solar system. He specialized in making detailed (and difficult) mathematical calculations of how orbits and motions change over geologic time. Figure 4.20 George Darwin (1845–1912). George Darwin is best known for studying Earth’s spin in relation to angular momentum. What Darwin calculated for the Earth-Moon system was that the Moon will slowly spiral outward, away from Earth. As it moves farther away, it will orbit less quickly (just as planets farther from the Sun move more slowly in their orbits). Thus, the month will get longer. Also, because the Moon will be more distant, total eclipses of the Sun will no longer be visible from Earth. Both the day and the month will continue to get longer, although bear in mind that the effects are very gradual. Darwin’s calculations were confirmed by mirrors placed on the Moon by Apollo 11 astronauts. These show that the Moon is moving away by 3.8 centimeters per year, and that ultimately—billions of years in the future—the day and the month will be the same length (about 47 of our present days). At this point the Moon will be stationary in the sky over the same spot on Earth, meaning some parts of Earth will see the Moon and its phases and other parts will never see them. This kind of alignment is already true for Pluto’s moon Charon (among others). Its rotation and orbital period are the same length as a day on Pluto. 128 Chapter 4 Earth, Moon, and Sky This OpenStax book is available for free at http://cnx.org/content/col11992/1.13
  37. 37. 4.7 ECLIPSES OF THE SUN AND MOON Learning Objectives By the end of this section, you will be able to: Describe what causes lunar and solar eclipses Differentiate between a total and partial solar eclipse Explain why lunar eclipses are much more common than solar eclipses One of the coincidences of living on Earth at the present time is that the two most prominent astronomical objects, the Sun and the Moon, have nearly the same apparent size in the sky. Although the Sun is about 400 times larger in diameter than the Moon, it is also about 400 times farther away, so both the Sun and the Moon have the same angular size—about 1/2°. As a result, the Moon, as seen from Earth, can appear to cover the Sun, producing one of the most impressive events in nature. Any solid object in the solar system casts a shadow by blocking the light of the Sun from a region behind it. This shadow in space becomes apparent whenever another object moves into it. In general, an eclipse occurs whenever any part of either Earth or the Moon enters the shadow of the other. When the Moon’s shadow strikes Earth, people within that shadow see the Sun at least partially covered by the Moon; that is, they witness a solar eclipse. When the Moon passes into the shadow of Earth, people on the night side of Earth see the Moon darken in what is called a lunar eclipse. Let’s look at how these happen in more detail. The shadows of Earth and the Moon consist of two parts: a cone where the shadow is darkest, called the umbra, and a lighter, more diffuse region of darkness called the penumbra. As you can imagine, the most spectacular eclipses occur when an object enters the umbra. Figure 4.21 illustrates the appearance of the Moon’s shadow and what the Sun and Moon would look like from different points within the shadow. Chapter 4 Earth, Moon, and Sky 129
  38. 38. Figure 4.21 Solar Eclipse. (a) The shadow cast by a spherical body (the Moon, for example) is shown. Notice the dark umbra and the lighter penumbra. Four points in the shadow are labeled with numbers. In (b) you see what the Sun and Moon would look like in the sky at the four labeled points. At position 1, you see a total eclipse. At positions 2 and 3, the eclipse is partial. At position 4, the Moon is farther away and thus cannot cover the Sun completely; a ring of light thus shows around the Sun, creating what is called an “annular” eclipse. If the path of the Moon in the sky were identical to the path of the Sun (the ecliptic), we might expect to see an eclipse of the Sun and the Moon each month—whenever the Moon got in front of the Sun or into the shadow of Earth. However, as we mentioned, the Moon’s orbit is tilted relative to the plane of Earth’s orbit about the Sun by about 5° (imagine two hula hoops with a common center, but tilted a bit). As a result, during most months, the Moon is sufficiently above or below the ecliptic plane to avoid an eclipse. But when the two paths cross (twice a year), it is then “eclipse season” and eclipses are possible. Eclipses of the Sun The apparent or angular sizes of both the Sun and Moon vary slightly from time to time as their distances from Earth vary. (Figure 4.21 shows the distance of the observer varying at points A–D, but the idea is the same.) Much of the time, the Moon looks slightly smaller than the Sun and cannot cover it completely, even if the two are perfectly aligned. In this type of “annular eclipse,” there is a ring of light around the dark sphere of the Moon. However, if an eclipse of the Sun occurs when the Moon is somewhat nearer than its average distance, the Moon can completely hide the Sun, producing a total solar eclipse. Another way to say it is that a total eclipse of the Sun occurs at those times when the umbra of the Moon’s shadow reaches the surface of Earth. 130 Chapter 4 Earth, Moon, and Sky This OpenStax book is available for free at http://cnx.org/content/col11992/1.13
  39. 39. The geometry of a total solar eclipse is illustrated in Figure 4.22. If the Sun and Moon are properly aligned, then the Moon’s darkest shadow intersects the ground at a small point on Earth’s surface. Anyone on Earth within the small area covered by the tip of the Moon’s shadow will, for a few minutes, be unable to see the Sun and will witness a total eclipse. At the same time, observers on a larger area of Earth’s surface who are in the penumbra will see only a part of the Sun eclipsed by the Moon: we call this a partial solar eclipse. Between Earth’s rotation and the motion of the Moon in its orbit, the tip of the Moon’s shadow sweeps eastward at about 1500 kilometers per hour along a thin band across the surface of Earth. The thin zone across Earth within which a total solar eclipse is visible (weather permitting) is called the eclipse path. Within a region about 3000 kilometers on either side of the eclipse path, a partial solar eclipse is visible. It does not take long for the Moon’s shadow to sweep past a given point on Earth. The duration of totality may be only a brief instant; it can never exceed about 7 minutes. Figure 4.22 Geometry of a Total Solar Eclipse. Note that our diagram is not to scale. The Moon blocks the Sun during new moon phase as seen from some parts of Earth and casts a shadow on our planet. Because a total eclipse of the Sun is so spectacular, it is well worth trying to see one if you can. There are some people whose hobby is “eclipse chasing” and who brag about how many they have seen in their lifetimes. Because much of Earth’s surface is water, eclipse chasing can involve lengthy boat trips (and often requires air travel as well). As a result, eclipse chasing is rarely within the budget of a typical college student. Nevertheless, a list of future eclipses is given for your reference in Appendix H, just in case you strike it rich early. (And, as you can see in the Appendix, there will be total eclipses visible in the United States in 2017 and 2024, to which even college students may be able to afford travel.) Appearance of a Total Eclipse What can you see if you are lucky enough to catch a total eclipse? A solar eclipse starts when the Moon just begins to silhouette itself against the edge of the Sun’s disk. A partial phase follows, during which more and more of the Sun is covered by the Moon. About an hour after the eclipse begins, the Sun becomes completely hidden behind the Moon. In the few minutes immediately before this period of totality begins, the sky noticeably darkens, some flowers close up, and chickens may go to roost. As an eerie twilight suddenly descends during the day, other animals (and people) may get disoriented. During totality, the sky is dark enough that planets become visible in the sky, and usually the brighter stars do as well. As the bright disk of the Sun becomes entirely hidden behind the Moon, the Sun’s remarkable corona flashes Chapter 4 Earth, Moon, and Sky 131
  40. 40. into view (Figure 4.23). The corona is the Sun’s outer atmosphere, consisting of sparse gases that extend for millions of miles in all directions from the apparent surface of the Sun. It is ordinarily not visible because the light of the corona is feeble compared with the light from the underlying layers of the Sun. Only when the brilliant glare from the Sun’s visible disk is blotted out by the Moon during a total eclipse is the pearly white corona visible. (We’ll talk more about the corona in the chapter on The Sun: A Garden-Variety Star.) Figure 4.23 The Sun’s Corona. The corona (thin outer atmosphere) of the Sun is visible during a total solar eclipse. (It looks more extensive in photographs than it would to the unaided eye.) (credit: modification of work by Lutfar Rahman Nirjhar) The total phase of the eclipse ends, as abruptly as it began, when the Moon begins to uncover the Sun. Gradually, the partial phases of the eclipse repeat themselves, in reverse order, until the Moon has completely uncovered the Sun. We should make one important safety point here: while the few minutes of the total eclipse are safe to look at, if any part of the Sun is uncovered, you must protect your eyes with safe eclipse glasses [2] or by projecting an image of the Sun (instead of looking at it directly). For more, read the How to Observe Solar Eclipses box in this chapter. Eclipses of the Moon A lunar eclipse occurs when the Moon enters the shadow of Earth. The geometry of a lunar eclipse is shown in Figure 4.24. Earth’s dark shadow is about 1.4 million kilometers long, so at the Moon’s distance (an average of 384,000 kilometers), it could cover about four full moons. Unlike a solar eclipse, which is visible only in certain local areas on Earth, a lunar eclipse is visible to everyone who can see the Moon. Because a lunar eclipse can be seen (weather permitting) from the entire night side of Earth, lunar eclipses are observed far more frequently from a given place on Earth than are solar eclipses. 2 Eclipse glasses are available in many planetarium and observatory gift stores, and also from the two main U.S. manufacturers: American Paper Optics and Rainbow Symphony. 132 Chapter 4 Earth, Moon, and Sky This OpenStax book is available for free at http://cnx.org/content/col11992/1.13

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